New method of solving problems of radiation transport theory. 1. General solution. Semiinfinite layer

1981 ◽  
Vol 41 (6) ◽  
pp. 1358-1366
Author(s):  
K. S. Adzerikho ◽  
N. V. Podluzhnyak ◽  
Yu. V. Khodyko
Keyword(s):  
General Solution ◽  
Transport Theory ◽  
Radiation Transport ◽  
New Method

scholarly journals Spectroscopy in heterogenous media and applications for bioprocess and environmental monitoring

2002 ◽  
Vol 4 (1) ◽  
pp. 21-26 ◽  
Author(s):  
Frank Schael ◽  
Oliver Reich ◽  
Sonja Engelhard
Keyword(s):  
Diffuse Reflectance ◽  
Near Infrared ◽  
Transport Theory ◽  
Radiation Transport ◽  
Diffusion Theory ◽  
Nile Blue ◽  
Milk Powder ◽  
Photon Migration ◽  
Heterogenous Media ◽  
Reflectance Measurements

Diffuse reflectance measurements and photon migration studies with near infrared (NIR) diode lasers were employed to elucidate experimental methods for determining absorption and scattering coefficients and species concentrations in heterogenous media. Measurements were performed at a number of wavelengths utilizing several laser sources some of which were widely tunable. In order to establish the applicability of simple photon migration models derived from radiation transport theory and to check the experimental boundary conditions of our measurements, simple light scattering solutions (such as suspensions of titanium dioxide, latex particles, and solutions of milk powder) containing dyes (such as nile blue, isosulfan blue) were investigated. The results obtained from diffuse-reflectance studies at different sourcedetector distances were in accordance with predictions from simple photon diffusion theory. Applications of reflectance measurements for monitoring of cell growth during fermentation processes and forin-situinvestigations of soils are presented.

Further Contributions to the Theory of Peripheral Jets in Ground Proximity

1992 ◽  
Vol 36 (01) ◽  
pp. 88-90
Author(s):  
David S. Tselnik
Keyword(s):  
General Solution ◽  
Infinite Series ◽  
Elliptic Functions ◽  
Jet Flow ◽  
New Method ◽  
Asymptotic Formulas ◽  
Flow Problems ◽  
Complicated Task

A number of plane inviscid jet flow problems of interest in hydrodynamics require the use of elliptic functions theory. Generally speaking, finding the general solution to a problem in terms of elliptic functions is not a complicated task. However, finding solutions as rapidly convergent infinite series or as sound asymptotic formulas is often not as easy, and special ways of treatment may prove to be necessary. In parallel with solving the problem of peripheral jets, the author's earlier paper (1985) proposed some such ways of treatment. In the present paper, a new method of treatment is proposed (and used);this approach may be of help in studies where the methods of elliptic functions theory have to be used.

A Recursive Householder Transformation for Complex Dynamical Systems With Constraints

1988 ◽  
Vol 55 (3) ◽  
pp. 729-734 ◽  
Author(s):  
F. M. L. Amirouche ◽  
Tongyi Jia ◽  
Sitki K. Ider
Keyword(s):  
Dynamical Systems ◽  
General Solution ◽  
Equations Of Motion ◽  
New Method ◽  
Systems Dynamics ◽  
Complex Dynamical Systems ◽  
Governing Equations ◽  
Householder Transformation ◽  
Constraint Equations ◽  
Computer Automation

A new method is presented by which equations of motion of complex dynamical systems are reduced when subjected to some constraints. The method developed is used when the governing equations are derived using Kane’s equations with undetermined multipliers. The solution vectors of the constraint equations are determined utilizing the recursive Householder transformation to obtain a Pseudo-Uptriangular matrix. The most general solution in terms of new independent coordinates is then formulated. Methods previously used for handling such systems are discussed and the new method advantages are illustrated. The procedures developed are suitable for computer automation and especially in developing generic programs to study a large class of systems dynamics such as robotics, biosystems, and complex mechanisms.

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